If #" "##((n), (k))=((n!), (k!(n-k)!))# #" "# show that #" "##((n), (k))=((n), (n-k))#...?

1 Answer
MattyMatty
Feb 15, 2018

#"See explanation"#

Explanation:

#"This is trivial."#
#((n), (k)) = ((n!),(k!(n-k)!))" (definition combination)"#
#=> color(red)(((n), (n-k))) = ((n!),((n-k)!(n-(n-k))!))#
# = ((n!),((n-k)!k!))" (n-(n-k) = n-n+k = 0+k = k)"#
# = ((n!),(k!(n-k)!))" (commutativity of multiplication)"#
# = color(red)(((n),(k)))" (definition combination)"#

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